A Common Subexpression Elimination Tree Algorithm

Al-Hasani, Firas; Hayes, Michael; Bainbridge-Smith, Andrew

doi:10.1109/tcsi.2013.2244328

Cited by 11 publications

(19 citation statements)

References 40 publications

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“…Al-Hasani et al [10] have represented CSE algorithm which is used to minimize the complexity of the MCM operation. MCM used binary signed digit (BSD) number system to design the coefficients.…”

Section: Literature Surveymentioning

confidence: 99%

Efficient Finite Impulse Response Filter Architecture Using Multiple Constant Multiplication and Common Sub-Expression Elimination Techniques

Shukla

Beulet

2017

Asian J Pharm Clin Res

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Objective: This paper introduces the computationally efficient, low power, high speed partial reconfigurable Finite impulse response (FIR) filter design using multiple constant multiplication technique (MCM). The complexity of many digital signal processing (DSP) systems is reduced by multiple constant multiplication operation.Methods: Multiple constant multiplications (MCM) along with methods like common sub expression elimination (CSE) is used for the better performance of digital signal processing systems. This paper introduces a CSE operation of finite Impulse response filter design which is solved with decreased number of operators.Results: Using these techniques shows that the area efficiency is increased when compared with designs based on direct form implementation of FIR filters. Conclusion:This method has achieved minimum area and delay with a high process rate. The future work will be for using CSE for 0-1 ILP.

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Section: Literature Surveymentioning

confidence: 99%

Efficient Finite Impulse Response Filter Architecture Using Multiple Constant Multiplication and Common Sub-Expression Elimination Techniques

Shukla

Beulet

2017

Asian J Pharm Clin Res

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“…The tree grows from the root node of value 47, which is at depth 0, towards leaves at depth L = 6 (from the least significant digit (LSD) toward the most significant digit (MSD)). Tree growth can be expressed by the recursion [5] [30]…”

Section: Decomposition Demand and Augmented Demand Graphsmentioning

confidence: 99%

“…The modulo operation v p ≡ d mod r partitions the digit set D into r disjoint sets [5]. Digits will be released from their disjoint sets when the modulo operation is applied at nodes.…”

Section: Decomposition Demand and Augmented Demand Graphsmentioning

confidence: 99%

“…This example shows the reason of considering the multiplier as a bottleneck element in DSP systems because it consumes a large area, high power, and has a long delay (critical path) [1]. To solve the multiplier problem, the MCM is designed to be free of the explicit multiplication (multiplierless) [5] [47] by using simpler logic operations of shift and add/subtract as shown in Fig. 2.…”

Section: Introductionmentioning

confidence: 99%

“…To the best of our knowledge, there is no combinatorial model in the literature that describes the MCM problem. In this work we develop such model using the subexpression space concept proposed in [5]. The individual subexpression spaces of coefficients and subexpressions are combined into one large space resulting in an acyclic directed graph called the decomposition graph.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Developing a combinatorial model for the multiple constant multiplication

Al-Hasani¹

2015

IJET

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A combinatoric model for the multiple constant multiplication (MCM) operation is developed. The model is found by decomposing each coefficient using the A−operation into two subexpressions. The constituted subexpressions are, in turn, decomposed using the A−operation. Connecting all of the decompositions results the decomposition graph which represents the solution space. The decomposition graph itself is not feasible for routing to find the minimum solutions. Therefore, a transformation on the A−operation is proposed to make the decomposition graph routable. In this case, the A−operation is transformed into a subexpression operation by replacing the shift information attached to the arcs by the other subexpression information which is called the demand. A demand that attached to an arc will represent its cost. The resulting transformed graph is called the demand graph. The demand graph is augmented with deadheading arcs to make it routable. Deadheading arcs are with zero demand. Similarly, traversing an arc with synthesized demand is of zero cost. Enumerating all of the routes that start from the signal vertex and visit all the coefficients gives all the solutions of the MCM problem. The routing technique requires redirecting the route when encountering an unsynthesized demand. The route in this case backtrack to the first encountered synthesized ancestors for this demand. This routing style analogous to the dynamic capacitated arc routing. To prevent exhaust routing, ant colony optimization (ACO) meta-heuristics is proposed to traverse the augmented demand graph. The solution space contains all the possible solutions that can be obtained from using both of the common subexpression elimination (CSE) and graph dependent heuristics that traditionally used to solve the MCM operation.

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Algorithms for Multiplierless Multiple Constant Multiplication in Online Arithmetic

Joseph¹,

Devanathan

2018

Circuits Syst Signal Process

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A Common Subexpression Elimination Tree Algorithm

Cited by 11 publications

References 40 publications

Efficient Finite Impulse Response Filter Architecture Using Multiple Constant Multiplication and Common Sub-Expression Elimination Techniques

Efficient Finite Impulse Response Filter Architecture Using Multiple Constant Multiplication and Common Sub-Expression Elimination Techniques

Developing a combinatorial model for the multiple constant multiplication

Algorithms for Multiplierless Multiple Constant Multiplication in Online Arithmetic

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